Plot Diagnostics for a Univariate EVD Object
Four plots (selectable by which) are currently provided:
a P-P plot, a Q-Q plot, a density plot and a return level plot.
## S3 method for class 'uvevd'
plot(x, which = 1:4, main, ask = nb.fig <
length(which) && dev.interactive(), ci = TRUE, cilwd = 1,
a = 0, adjust = 1, jitter = FALSE, nplty = 2, ...)x |
An object that inherits from class |
which |
If a subset of the plots is required, specify a
subset of the numbers |
main |
Title of each plot. If given, must be a character
vector with the same length as |
ask |
Logical; if |
ci |
Logical; if |
cilwd |
Line width for confidence interval lines. |
a |
Passed through to |
adjust, jitter, nplty |
Arguments to the density plot.
The density of the fitted model is plotted with a rug plot and
(optionally) a non-parameteric estimate. The argument
|
... |
Other parameters to be passed through to plotting functions. |
The following discussion assumes that the fitted model is stationary. For non-stationary generalized extreme value models the data are transformed to stationarity. The plot then corresponds to the distribution obtained when all covariates are zero.
The P-P plot consists of the points
{(G_n(z_i), G(z_i)), i = 1,…,m}
where G_n is the empirical distribution function
(defined using ppoints), G is the model based
estimate of the distribution (generalized extreme value
or generalized Pareto), and z_1,…,z_m are the data
used in the fitted model, sorted into ascending order.
The Q-Q plot consists of the points
{(G^{-1}(p_i), z_i), i = 1,…,m}
where G^{-1} is the model based estimate of the quantile
function (generalized extreme value or generalized Pareto),
p_1,…,p_m are plotting points defined by
ppoints, and z_1,…,z_m are the data
used in the fitted model, sorted into ascending order.
The return level plot for generalized extreme value models is defined as follows.
Let G be the generalized extreme value distribution function, with location, scale and shape parameters a, b and s respectively. Let z_t be defined by G(z_t) = 1 - 1/t. In common terminology, z_t is the return level associated with the return period t.
Let y_t = -1/log(1 - 1/t). It follows that
z_t = a + b((y_t)^s - 1)/s.
When s = 0, z_t is defined by continuity, so that
z_t = a + b log(y_t).
The curve within the return level plot is z_t plotted against y_t on a logarithmic scale, using maximum likelihood estimates of (a,b,s). If the estimate of s is zero, the curve will be linear. For large values of t, y_t is approximately equal to the return period t. It is usual practice to label the x-axis as the return period.
The points on the plot are
{(-1/log(p_i), z_i), i = 1,…,m}
where p_1,…,p_m are plotting points defined by
ppoints, and z_1,…,z_m are the data
used in the fitted model, sorted into ascending order.
For a good fit the points should lie “close” to the curve.
The return level plot for peaks over threshold models is defined as follows.
Let G be the generalized Pareto distribution function,
with location, scale and shape parameters u, b
and s respectively, where u is the model threshold.
Let z_m denote the m period return level
(see fpot and the notation therein).
It follows that
z_m = u + b((pmN)^s - 1)/s.
When s = 0, z_m is defined by continuity, so that
z_m = u + b log(pmN).
The curve within the return level plot is z_m plotted against m on a logarithmic scale, using maximum likelihood estimates of (b,s,p). If the estimate of s is zero, the curve will be linear.
The points on the plot are
{(1/(pN(1-p_i)), z_i), i = 1,…,m}
where p_1,…,p_m are plotting points defined by
ppoints, and z_1,…,z_m are the data
used in the fitted model, sorted into ascending order.
For a good fit the points should lie “close” to the curve.
uvdata <- rgev(100, loc = 0.13, scale = 1.1, shape = 0.2) M1 <- fgev(uvdata) ## Not run: par(mfrow = c(2,2)) ## Not run: plot(M1) uvdata <- rgpd(100, loc = 0, scale = 1.1, shape = 0.2) M1 <- fpot(uvdata, 1) ## Not run: par(mfrow = c(2,2)) ## Not run: plot(M1)
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